Results 31 to 40 of about 8,395 (199)
Lp‐Curvature Measures and Lp,q‐Mixed Volumes
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 Motivated by Lutwak et al.’s Lp‐dual curvature measures, we introduce the concept of Lp‐curvature measures. This new Lp‐curvature measure is an extension of the classical surface area measure, Lp‐surface area measure, and curvature measure. In this paper, we first prove some properties of the Lp‐curvature measure.
Tongyi Ma, Raúl E. Curto
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Numerical methods for the hyperbolic Monge-Ampère equation based on the method of characteristics [PDF]
Partial Differential Equations and Applications, 2021 We present three alternative derivations of the method of characteristics (MOC) for a second order nonlinear hyperbolic partial differential equation (PDE) in two independent variables.
Maikel W. M. C. Bertens +4 more
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New Results on the Radial Solutions to a Class of Nonlinear k‐Hessian System
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 This paper investigates the positive radial solutions of a nonlinear k‐Hessian system. ΛSk1/kλD2z1Sk1/kλD2z1=bxφz1,z2, x∈ℝNΛSk1/kλD2z2Sk1/kλD2z2=hxψz1,z2, x∈ℝN, where Λ is a nonlinear operator and b, h, φ, ψ are continuous functions. With the help of Keller–Osserman type conditions and monotone iterative technique, the positive radial solutions of the ...
Guotao Wang +2 more
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Generalized Liouville theorem for viscosity solutions to a singular Monge-Ampère equation
Advances in Nonlinear Analysis, 2023 In this article, we study the asymptotic behaviour at infinity for viscosity solutions to a singular Monge-Ampère equation in half space from affine geometry.
Jian Huaiyu, Wang Xianduo
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Newton Linearization of the Curvature Operator in Structured Grid Generation with Sample Solutions
International Journal of Mathematics and Mathematical Sciences, Volume 2022, Issue 1, 2022., 2022 Elliptic grid generation equations based on the Laplacian operator have the well‐known property of clustering the mesh near convex boundaries and declustering it near concave boundaries. In prior work, a new differential operator was derived and presented to address this issue.
Pat Piperni +2 more
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The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge-Ampère Equation
Abstract and Applied Analysis, 2013 We consider the existence, uniqueness, and asymptotic behavior of a classical solution to the initial and Neumann boundary value problem for a class nonlinear parabolic equation of Monge-Ampère type. We show that such solution exists for all times and is
Juan Wang, Jinlin Yang, Xinzhi Liu
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The Monge–Ampère equation for non-integrable almost complex structures [PDF]
Journal of the European Mathematical Society (Print), 2016 We show existence and uniqueness of solutions to the Monge-Ampere equation on compact almost complex manifolds with non-integrable almost complex structure.
Jianchun Chu +2 more
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Interior $C^2$ estimate for Monge-Ampère equation in dimension two [PDF]
, 2020 We obtain a genuine local $C^2$ estimate for the Monge-Ampere equation in dimension two, by using the partial Legendre transform.
Jiakun Liu
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Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties [PDF]
, 2012 We show, using a direct variational approach, that the second boundary value problem for the Monge-Amp\`ere equation in R^n with exponential non-linearity and target a convex body P is solvable iff 0 is the barycenter of P.
Berman, Robert J., Berndtsson, Bo
core +4 more sources
Advanced Nonlinear Studies, 2018 This paper is concerned with the boundary behavior of the unique convex solution to a singular Dirichlet problem for the Monge–Ampère ...
Zhang Zhijun
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